07/10/2018

Delay of gratification (marshmallow study replication)

Her school achievement later in life can be predicted from her ability to wait for a treat (or by her family's SES). Photo: Manley099/Getty Images

There's a new replication study about the famous "marshmallow study", and it's all over the popular press. You've probably heard of the original research: Kids are asked to sit alone in a room with a single marshmallow (or some other treat they like, such as pretzels). If the child can wait for up to 15 minutes until the experimenter comes back, they receive two marshmallows. But if they eat the first one early, they don't. As part of the original study, kids were tracked over several years. One of the key findings was that the longer children were able to wait at age 4, the better they were doing in school as teenagers. Psychologists have often used this study as an illustration of how self-control is related to important life outcomes.

The press coverage of this year's replication study illustrates at least two things. First, it's a nice example of multiple regression. Second, it's an example of how different media outlets assign catchy--but sometimes erroneous--headlines on the same study.

First, let's talk about the multiple regression piece. Regression analyses often try to understand a core bivariate relationship more fully. In this case, the core relationship they start with is between the two variables, "length of time kids waited at age 4" and "test performance at age 15." Here's how it was described by Payne and Sheeran in the online magazine Behavioral Scientist:

The result? Kids who resisted temptation longer on the marshmallow test had higher achievement later in life. The correlation was in the same direction as in Mischel’s early study. It was statistically significant, like the original study. The correlation was somewhat smaller, and this smaller association is probably the more accurate estimate, because the sample size in the new study was larger than the original. Still, this finding says that observing a child for seven minutes with candy can tell you something remarkable about how well the child is likely to do in high school.

a) Sketch a well-labelled scatterplot of the relationship described above. What direction will the dots slope? Will they be fairly tight to a straight line, or spread out?

b) The writers (Payne and Sheeran) suggest that a larger sample size leads to a more accurate estimate of a correlation. Can you explain why a large sample size might give a more accurate statistical estimate? (Hint: Chapter 8 talks about outliers and sample size--see Figures 8.10 and 8.11.)

Now here's more about the study:

The researchers next added a series of “control variables” using regression analysis. This statistical technique removes whatever factors the control variables and the marshmallow test have in common. These controls included measures of the child’s socioeconomic status, intelligence, personality, and behavior problems. As more and more factors were controlled for, the association between marshmallow waiting and academic achievement as a teenager became nonsignificant.

c) What's proposed above is that social class is a third variable ("C") that might be associated with both waiting time ("A") and school achievement ("B"). Using Figure 8.15. draw this proposal. Think about it, too: Why does it make sense that lower SES might go both with lower waiting time (A)? Why might lower SES go with lower school achievement (B)?

d) Now create a mockup regression table that might fit the pattern of results being described above. Put the DV at the top (what is the DV?), then list the predictor variables underneath, starting with Waiting time at Age 4, and including things like Child's Socioeconomic Status and Intelligence. Which betas should be significant? Which should not?

Basically, here we have a core bivariate relationship (between wait time and later achievement), and then a critic suggests a possible third variable (SES). They used regression to see if the core relationship was still there when the third variable was controlled for. The core relationship went away, suggesting that SES was a third variable that can help explain why kids who wait longer do better in school later on.

Next let's talk about some of the hype around this replication study. The Behavioral Scientist piece (quoted above) is one of the more balanced descriptions. Its headline was, Try to Resist Misinterpreting the Marshmallow Test. It emphasized that the core relationship was replicated. It also explains in some detail why SES is related to self-control, and how the two probably cannot be meaningfully separated--it's a nuanced report. But other press coverage had a doomsday feel:

One person on Twitter even wrote,"The marshmallow/delayed gratification study always felt "wrong" to me - this year it was reported to be hopelessly flawed"

Are these headlines and comments fair? Probably not. As Payne and Sheeran write in Behavioral Scientist,

The problem is that scholars have known for decades that affluence and poverty shape the ability to delay gratification. Writing in 1974, Mischel observed that waiting for the larger reward was not only a trait of the individual but also depended on people’s expectancies and experience. If researchers were unreliable in their promise to return with two marshmallows, anyone would soon learn to seize the moment and eat the treat. He illustrated this with an example of lower-class black residents in Trinidad who fared poorly on the test when it was administered by white people, who had a history of breaking their promises. Following this logic, multiple studies over the years have confirmed that people living in poverty or who experience chaotic futures tend to prefer the sure thing now over waiting for a larger reward that might never come. But if this has been known for years, where is the replication crisis?

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